Answer
$2$ examples: $\frac{1}{x}$ and $\frac{2}{3x}$
$LCD=3x$
sum: $\frac{5}{3x}$.
Work Step by Step
An example of two rational expressions with different denominators are $\frac{1}{x}$ and $\frac{2}{3x}$.
The $LCD$ of $x$ and $3x$ is $3x$ since it is the simplest expression that can be exactly divided both by $3$ and $x$.
The sum is given by
$$
\frac{1}{x}+\frac{2}{3x}
.$$
Changing the two rational expressions to equivalent rational expressions that use the $LCD$, then
$$\begin{aligned}
\frac{1}{x}+\frac{2}{3x}&=
\frac{1}{x}\cdot\frac{3}{3}+\frac{2}{3x}
\\&=
\frac{3}{3x}+\frac{2}{3x}
.\end{aligned}
$$
Adding/Subtracting similar fractions involves adding/subtracting the numerators and copying the common denominator. Therefore,
$$\begin{aligned}
\frac{3}{3x}+\frac{2}{3x}&=
\frac{5}{3x}
\end{aligned}
.$$Hence, the sum of the two rational expressions is $\frac{5}{3x}$.
